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Second Interim Report
Clair Brown, Editor

12. Enhancing the Rate of Learning by Doing Through Human Resource Management
Nile W. Hatch

12.4 Empirical Analysis

The cumulative volume variable is constructed as the sum of wafer starts from the initial observation to the current period. The number of wafer starts for a particular process each month or quarter is reported in the questionnaire." For convenience in estimation, the cumulative volume variable is scaled in the regression to represent units of 1000 wafers.

Unfortunately, the number of full-time engineers devoted to the process during the period is not reported in the questionnaire. In fact, it is clear from interviews during follow-up visits that this information is not known. The fabs invariably reported that they do not track the time spent by engineering staff on individual processes, but rather that engineers work on the most pressing problems. In order to estimate the influence of cumulative engineering on yields, we employ a rule to allocate the engineering staff to processes. If there are no new processes in the fab, each process is allocated a share of total engineering full time equivalents (FTES) that is proportional to the share of total volume accounted for by that process. If a new process has been introduced, we assume that the new process receives 75% of the engineering FTEs for the first year and then receives its portion of engineering according to its relative volume.

While this allocation scheme is ad-hoc. it is consistent with what fabs report their engineers are doing, namely focus attention where the greatest problems are. In the months required to "characterize" and "ramp-up" a new process, the most pressing problems arise with the new process and many of the fab's engineering resources are devoted to the effort. When there are no new processes in the fab, our allocation rule is conservative with respect to estimating the effect of engineering on learning. This is because in general 7 newer processes have relatively lower volumes but require more engineering effort in adjusting process specification limits.

The clean room grade is the maximum number of particles per cubic foot of clean room area. The number of mask layers reports the number of layers that include the imprinting of patterns through steps called photolithography. Both of these variables are reported in the CSM questionnaire. The equipment vintage is defined as the original purchase date of the machine averaged over all machines in the fab. Equipment installation dates are given in the questionnaire, however in some cases, fabs purchased and installed used equipment rather than new. In those situations, the original purchase date of the equipment was obtained through follow-up requests.

"The earliest fabs in the CSM study were requested to report quarterly historic data on volume and yields. Subsequently the questionnaire was revised to elicit monthly data. This does not cause a problem for estimating the learning curve as Iona as all the variables are defined by the appropriate period length.

The data for the team participation and turnover variables introduced in equations (12.8) - (12.9) were obtained from interviews conducted during visits to the fabs. The team involvement variable gives an estimate of the share of operators involved in teams. The operator turnover variable is the average annual percentage of operators that are replaced.

Regression results for the human capital specifications of the defect density learning curve are reported in table 12.1. Each curve is estimated using a nonlinear maximum likelihood estimator." The number of observations, (n) and the R 2 between the observed and predicted values are also reported. The results for equation (12.7) are reported in this table for the sake of comparison.

The regression results for the basic learning by doing model (equation (12.6)) are presented in the first column of Table 12.1. The cumulative volume variable is shown to improve the defect density but not significantly." The cumulative engineering variable is significant in reducing the defect density. This result underscores the importance of engineering analysis as a determinant of learning by doing in semiconductor manufacturing and reiterates the idea that benefits of learning do not come from repetition, but rather from deliberate activities aimed at learning. The estimated coefficients a and P define the rate of learning by doing for the fabs in the sample. The estimates also show that the defect density is increasing in the clean room grade-more particles in the manufacturing environment increases the risk of defects. The number of mask layers is also significant in increasing the defect density. This " is because more processing steps increase the likelihood of processing errors and particle defects. As new equipment is installed and the equipment vintage increases, the defect density falls significantly. This result is attributable to the superior process control associated with newer equipment.

The disruptive effect of new equipment installations is also considered in the estimates for equation (12.7). The result is precisely what was hypothesized, namely that defect density values increase significantly in periods when new equipment is installed into the fab. Unfamiliarity with the new equipment leads to parametric processing defects until the processing characteristics of the new equipment can be discovered through experimentation. The defect density spike may also be associated

"The initial parameters were varied over a wide range to ensure that the estimates represent the global maximum of the likelihood function.

"Because of the functional forms used, a positive coefficient on variables included in the learning index, i.e., hl(Lt), reduces the defect density. For variables in the static component of the defect density curve h2('), a positive coefficient increases the defect density with an increase in particles in the clean room as, the installation activities are likely to introduce extra particles into the manufacturing environment.

The level of defect density is significantly reduced with increasing involvement of operators in problem-solving teams. When operators participate in solving problems and making decisions, more knowledge is available for yield improvement analysis than is otherwise possible. We see that the impact of team participation on the rate of learning from cumulative volume is negligible. We see a significant, negative coefficient associated with the interaction between cumulative engineering and team involvement. Once again the explanation lies in the level of defect density reduction and the diminishing marginal return to engineering analysis. When operators are performing the yield improvement activities for the simplest sources of yield losses, engineers are left with the more difficult problems where more analysis is required to obtain the same level of yield improvements. Engineers in fabs where the is a higher degree of team involvement by operators are operating further down the learning curve than their counterparts in other fabs and obtain a smaller marginal improvement of defect density for their efforts.

Turnover is a particularly demoralizing problem with respect to the fab's learning by doing efforts. The estimates of the turnover specification of the defect curve (equation (12.9)) show that the level of defect density rises with the turnover rate. This verifies the idea that turnover represents a loss of human capital. If high turnover continues over a Ion-, period, however, the fab will remain relatively overpopulated with,, operators that cause yield problems rather than solve them. Most fabs with high turnover rates (50% or more) find that they cannot utilize operators in their yield improvement efforts because they are not qualified. Instead, they must substitute some combination of engineers, technicians, and physical capital for operator problem-solving skills and try to train their operators as quickly as possible.

It might seem that when defect densities are high because operator turnover, engineering analysis would be more productive. After all, the yield losses caused by operators are relatively obvious. The estimates from the turnover equation show that the opposite is true-the rate of learning by doing through cumulative engineering is slowed. The reason for this is that engineering analysis is particularly unsuited for solving yield problems caused by inexperience. For one thing, continuously high turnover doesn't allow engineers to implement permanent solutions as they can with parametric or particle defects. Also, when the engineers are working with operators, they spend their time in training and mentoring trying to prevent yield losses. These activities reduce the opportunities for analysis that results in permanent solutions to problems. In this light, the true damage of operator turnover is apparent as we can see that turnover not only reduces the level of yield, but also reduces the rate of improvement.

Finally, in contrast to engineering analysis, the cumulative volume variable significantly increases the rate of learning by doing as turnover rises. It seems likely that because engineering attention is diverted from yield improvement to training, production volume becomes a relatively more important source of information for yield improvement. Given that the estimated coefficient for the cumulative volume/turnover interaction is an order of magnitude larger than the other learning variables, it would appear that the informational role of manufacturing volume is especially important when turnover is high.

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